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Topic: Matheology � 258
Replies: 104   Last Post: May 5, 2013 2:26 PM

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 JT Posts: 1,448 Registered: 4/7/12
Re: Matheology § 258
Posted: May 1, 2013 5:45 PM

On 1 Maj, 23:31, Dan <dan.ms.ch...@gmail.com> wrote:
> On May 1, 11:18 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>
>
>
>
>
>
>
>
>

> > On 1 Mai, 18:27, Dan <dan.ms.ch...@gmail.com> wrote:
>
> > > They have similar formulas,but behave in different ways .
> > > You would be correct in affirming that  b_inf = 1/9 is not part of the
> > > list .

>
> > Of course. It is not part of the list, because it cannot be written as
> > decimal number. Proof: All decimal numbers that can be written in this
> > form *are already in the list*. And there is no reason why 1/9 should
> > be missing, if it could be a decimal fraction.

>
> > > If it were part of the list , then a_inf would be a well-behaved
> > > natural number , but it isn't .

>
> > It is neither well behaved nor a natural number. The sequence 0.111...
> > does not exist other than by a finite name or formula.

>
> > > Limits only work properly with real numbers, not natural numbers .
>
> > Yes, that is true. But (and please read this very attentively!):
> > Cantor's argument requires the existence of the complete sequence
> > 0.111.... in digits:

>
> > You can see this easily here:
>
> > The list
>
> > 0.0
> > 0.1
> > 0.11
> > 0.111
> > ...

>
> > when replacing 0 by 1 has an anti-diagonal, the FIS of which are
> > always in the next line. So the anti-diagonal is not different from
> > all lines, unless it has an infinite sequence of 1's. But, as we just
> > saw, this is impossible.

>
> > Regards, WM
>
> I see no significant difference between referring to a mathematical
> object by a formula and referring to it by 'writing it down' .
> Writing it down , when possible , is just another formula for it.
> "1296"  , and  "36 * 36" , are both references to the same object ,
> and neither of them is "more true of a name" for the object than the
> other .
>
> Just like "1296" is "36 * 36" , and we can substitute one for another
> in mathematical expressions , and maintain their truth ,
> so is "1/9"  the same as  "0. the infinite sequence of 1's" . That we
> cannot truly  write down the name of the second expression is of no
> relevance. The most important point is that 'names for the same
> object , whether finite or infinite, are fully interchangeable'
>
> Since
> "0. the infinite sequence of 1's" is the same as  "1/9" then
>
> "The third digit of 0. the infinite sequence of 1's" is the same as
> "The third digit  of 1/9" is the same as "1" .
>
> Same object . Different names .Since we treat all possible names of
> the object the same , whether it be "a formula for the object" , or an
> "enumeration of its digits" , we never run into problems. And in every
> name for an object we can recover every other name, if we so wish .
>
> "1+3" = " 2+2" = "3+1" = "8-4" = "2*2" = "4" =  "00 ..... 04"
>
> "A rose by any other name would smell as sweet"

No no no a formula is not a number... A function is not a number... An
expression can be evaluated into a number. But 8 is a number 2*4 is an
expression 4+4 is an expression 2^3 is an expression they are all
different expressions/calculations leading to same value.

Date Subject Author
4/29/13 Virgil
4/29/13 mueckenh@rz.fh-augsburg.de
4/29/13 Virgil
4/30/13 dan.ms.chaos@gmail.com
4/30/13 mueckenh@rz.fh-augsburg.de
4/30/13 dan.ms.chaos@gmail.com
4/30/13 mueckenh@rz.fh-augsburg.de
4/30/13 Virgil
5/1/13 dan.ms.chaos@gmail.com
5/1/13 mueckenh@rz.fh-augsburg.de
5/1/13 dan.ms.chaos@gmail.com
5/1/13 mueckenh@rz.fh-augsburg.de
5/1/13 dan.ms.chaos@gmail.com
5/1/13 mueckenh@rz.fh-augsburg.de
5/1/13 dan.ms.chaos@gmail.com
5/1/13 mueckenh@rz.fh-augsburg.de
5/1/13 Virgil
5/1/13 mueckenh@rz.fh-augsburg.de
5/1/13 dan.ms.chaos@gmail.com
5/1/13 mueckenh@rz.fh-augsburg.de
5/1/13 dan.ms.chaos@gmail.com
5/1/13 mueckenh@rz.fh-augsburg.de
5/1/13 Virgil
5/1/13 dan.ms.chaos@gmail.com
5/1/13 JT
5/2/13 mueckenh@rz.fh-augsburg.de
5/2/13 Ed Prochak
5/2/13 Virgil
5/2/13 mueckenh@rz.fh-augsburg.de
5/2/13 dan.ms.chaos@gmail.com
5/2/13 mueckenh@rz.fh-augsburg.de
5/2/13 Virgil
5/3/13 dan.ms.chaos@gmail.com
5/3/13 mueckenh@rz.fh-augsburg.de
5/3/13 dan.ms.chaos@gmail.com
5/3/13 Virgil
5/3/13 mueckenh@rz.fh-augsburg.de
5/3/13 dan.ms.chaos@gmail.com
5/3/13 mueckenh@rz.fh-augsburg.de
5/3/13 dan.ms.chaos@gmail.com
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5/4/13 mueckenh@rz.fh-augsburg.de
5/4/13 dan.ms.chaos@gmail.com
5/4/13 mueckenh@rz.fh-augsburg.de
5/4/13 dan.ms.chaos@gmail.com
5/4/13 mueckenh@rz.fh-augsburg.de
5/4/13 dan.ms.chaos@gmail.com
5/4/13 mueckenh@rz.fh-augsburg.de
5/4/13 dan.ms.chaos@gmail.com
5/4/13 ross.finlayson@gmail.com
5/5/13 LudovicoVan
5/5/13 fom
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5/5/13 ross.finlayson@gmail.com
5/5/13 mueckenh@rz.fh-augsburg.de
5/5/13 Virgil
5/5/13 dan.ms.chaos@gmail.com
5/5/13 mueckenh@rz.fh-augsburg.de
5/4/13 Virgil
5/5/13 mueckenh@rz.fh-augsburg.de
5/5/13 Virgil
5/4/13 Virgil
5/4/13 Virgil
5/5/13 mueckenh@rz.fh-augsburg.de
5/5/13 Virgil
5/5/13 mueckenh@rz.fh-augsburg.de
5/4/13 fom
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5/4/13 ross.finlayson@gmail.com
5/4/13 Virgil
5/4/13 Virgil
5/4/13 Virgil
5/4/13 trj
5/4/13 Virgil
5/3/13 Virgil
5/3/13 Virgil
5/3/13 fom
5/3/13 dan.ms.chaos@gmail.com
5/3/13 fom
5/3/13 gus gassmann
5/3/13 Virgil
5/2/13 Virgil
5/1/13 Virgil
5/1/13 JT
5/1/13 Virgil
5/1/13 JT
5/1/13 Bergholt Stuttley Johnson
5/1/13 rt servo
5/1/13 mueckenh@rz.fh-augsburg.de
5/1/13 Virgil
5/1/13 Virgil
5/1/13 Virgil
5/1/13 Virgil
5/1/13 Virgil
4/30/13 Virgil
4/30/13 mueckenh@rz.fh-augsburg.de
4/30/13 Virgil
4/29/13 ross.finlayson@gmail.com
4/29/13 Virgil